Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control

We develop a compound decision theory framework for multiple-testing problems and derive an oracle rule based on the z values that minimizes the false nondiscovery rate (FNR) subject to a constraint on the false discovery rate (FDR). We show that many commonly used multiple-testing procedures, which...

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Veröffentlicht in:Journal of the American Statistical Association Jg. 102; H. 479; S. 901 - 912
Hauptverfasser: Sun, Wenguang, Cai, T. Tony
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Alexandria, VA Taylor & Francis 01.09.2007
American Statistical Association
Taylor & Francis Ltd
Schlagworte:
Adaptive procedure
Applications
Applied statistics
Compound decision rule
Decision analysis
Decision making
Decision theory
Density estimation
Discovery
Exact sciences and technology
False discovery rate
False positive errors
General topics
HIV
Human immunodeficiency virus
Hypothesis testing
Local false discovery rate
Mathematical procedures
Mathematics
Monotone likelihood ratio
Multivariate analysis
Null hypothesis
Oracles
P values
Probability and statistics
Proportions
Rules
Sciences and techniques of general use
Significance tests
Statistical methods
Statistical models
Statistics
Tests
Theory and Methods
Weighted classification
Non parametric estimation
Multivariate analysis
Microarray
Multiple decision
Hypothesis test
Statistical test
Law of large numbers
P value
Oracle
Compound decision rule
Human
Adaptive procedure
Data analysis
Retroviridae
Statistical estimation
Statistical decision
Monotone likelihood ratio
Lentivirus
Decision rule
Weighted classification
Virus
Statistical method
Decision theory
Local false discovery rate
False discovery rate
Human immunodeficiency virus
Application
ISSN:0162-1459, 1537-274X
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:We develop a compound decision theory framework for multiple-testing problems and derive an oracle rule based on the z values that minimizes the false nondiscovery rate (FNR) subject to a constraint on the false discovery rate (FDR). We show that many commonly used multiple-testing procedures, which are p value-based, are inefficient, and propose an adaptive procedure based on the z values. The z value-based adaptive procedure asymptotically attains the performance of the z value oracle procedure and is more efficient than the conventional p value-based methods. We investigate the numerical performance of the adaptive procedure using both simulated and real data. In particular, we demonstrate our method in an analysis of the microarray data from a human immunodeficiency virus study that involves testing a large number of hypotheses simultaneously.
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ISSN:0162-1459
1537-274X
DOI:10.1198/016214507000000545